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dsprfs (3)
  • >> dsprfs (3) ( Solaris man: Библиотечные вызовы )
  • 
    NAME
         dsprfs - improve the computed solution to a system of linear
         equations  when the coefficient matrix is symmetric indefin-
         ite and packed, and provides error bounds and backward error
         estimates for the solution
    
    SYNOPSIS
         SUBROUTINE DSPRFS( UPLO, N, NRHS, AP, AFP, IPIV, B, LDB,  X,
                   LDX, FERR, BERR, WORK, IWORK, INFO )
    
         CHARACTER UPLO
    
         INTEGER INFO, LDB, LDX, N, NRHS
    
         INTEGER IPIV( * ), IWORK( * )
    
         DOUBLE PRECISION AFP( * ), AP( * ), B( LDB, * ), BERR( *  ),
                   FERR( * ), WORK( * ), X( LDX, * )
    
    
    
         #include <sunperf.h>
    
         void dsprfs(char uplo, int n, int nrhs, double *dap,  double
                   *afp,  int  *ipivot,  double  *db, int ldb, double
                   *dx, int ldx,  double  *ferr,  double  *berr,  int
                   *info);
    
    PURPOSE
         DSPRFS improves the computed solution to a system of  linear
         equations  when the coefficient matrix is symmetric indefin-
         ite and packed, and provides error bounds and backward error
         estimates for the solution.
    
    
    ARGUMENTS
         UPLO      (input) CHARACTER*1
                   = 'U':  Upper triangle of A is stored;
                   = 'L':  Lower triangle of A is stored.
    
         N         (input) INTEGER
                   The order of the matrix A.  N >= 0.
    
         NRHS      (input) INTEGER
                   The number of right hand sides, i.e.,  the  number
                   of columns of the matrices B and X.  NRHS >= 0.
    
         AP        (input)   DOUBLE   PRECISION   array,    dimension
                   (N*(N+1)/2)
                   The upper  or  lower  triangle  of  the  symmetric
                   matrix  A,  packed  columnwise  in a linear array.
                   The j-th column of A is stored in the array AP  as
                   follows:   if  UPLO  =  'U',  AP(i  + (j-1)*j/2) =
                   A(i,j) for 1<=i<=j; if UPLO  =  'L',  AP(i  +  (j-
                   1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
    
         AFP       (input)   DOUBLE   PRECISION   array,    dimension
                   (N*(N+1)/2)
                   The factored form of the matrix A.   AFP  contains
                   the  block  diagonal  matrix D and the multipliers
                   used to obtain the factor U or L from the factori-
                   zation A = U*D*U**T or A = L*D*L**T as computed by
                   DSPTRF, stored as a packed triangular matrix.
    
         IPIV      (input) INTEGER array, dimension (N)
                   Details of the interchanges and the  block  struc-
                   ture of D as determined by DSPTRF.
    
         B         (input)   DOUBLE   PRECISION   array,    dimension
                   (LDB,NRHS)
                   The right hand side matrix B.
    
         LDB       (input) INTEGER
                   The leading dimension of  the  array  B.   LDB  >=
                   max(1,N).
    
         X         (input/output) DOUBLE PRECISION  array,  dimension
                   (LDX,NRHS)
                   On entry, the solution matrix X,  as  computed  by
                   DSPTRS.  On exit, the improved solution matrix X.
    
         LDX       (input) INTEGER
                   The leading dimension of  the  array  X.   LDX  >=
                   max(1,N).
    
         FERR      (output) DOUBLE PRECISION array, dimension (NRHS)
                   The estimated forward error bound for  each  solu-
                   tion  vector X(j) (the j-th column of the solution
                   matrix  X).   If  XTRUE  is  the   true   solution
                   corresponding  to  X(j),  FERR(j)  is an estimated
                   upper bound for the magnitude of the largest  ele-
                   ment in (X(j) - XTRUE) divided by the magnitude of
                   the largest element in X(j).  The estimate  is  as
                   reliable  as the estimate for RCOND, and is almost
                   always a slight overestimate of the true error.
    
         BERR      (output) DOUBLE PRECISION array, dimension (NRHS)
                   The componentwise relative backward error of  each
                   solution  vector X(j) (i.e., the smallest relative
                   change in any element of A or B that makes X(j) an
                   exact solution).
    
         WORK      (workspace)  DOUBLE  PRECISION  array,   dimension
                   (3*N)
    
         IWORK     (workspace) INTEGER array, dimension (N)
    
         INFO      (output) INTEGER
                   = 0:  successful exit
                   < 0:  if INFO = -i, the i-th argument had an ille-
                   gal value
    
    
    
    


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